His stuff: Depends on the facility, so long as its not overly garish, he should be able to display his art on the walls, could probably keep his clothes (so long as they're in good condition and not too ill fitting), and maybe one or two toys provided they can't be broken to be used as a weapon. The sheets are a no, not because they can't have MLP sheets, but more than likely just because they don't fit the bed and that can pose a hazard by allowing things to be easier to conceal. I don't, however, believe he would be able to keep the medallion, as it possesses a risk of becoming a choking hazard for others and himself should he try to forever sleep.
Hygiene: Usually they ensure at least one shower a day is taken and that teeth brushing is done. Depends on the facility though, some facilities have the right to force you to bathe, while others severely restrict you if you don't. Facilities are also set up to deal with his other hygiene issues as they almost always have adult diapers on hand and can force the usage of them if needed.
Chores: Uh... maybe, depends on how functioning they consider him. I can't really judge by Virginia standards, but the facility I work for would definitely have him doing chores.
No, at least they have never pushed religious beliefs on anyone when I was around. Because it is, I don't know, I just know the computer is in a communal space and nobody wants to see anyone choking the chicken while on shift or forced to live in a home (for the most part at least, I'm sure there's someone who enjoys that stuff).
Medication: Depends on the person and if the facility has a doctor on staff, I can't really touch on this stuff for HIPAA stuff, but what I can say is that if a doctor deems it necessary, it can be done.
Right to leave: Depends, what I am wondering is if they are considering setting up a conservatorship for Chris. If they do that and succeed, he does not have a right to leave should his conservator say he has to remain there. If they don't get a conservatorship, he technically does, unless there is some stipulation in the case that says he has to stay there or face actual charges for his crime (which I would hope they are smart enough to put in there).
Life in facility: See, I don't know there. I don't feel like diving into Virginia state law, but my guess would be probably not (at least not without conservatorship). I would think that all they could legally do is keep him there for the duration of his probation (or however long they could sentence him for the crime). If they get the conservatorship, then theoretically yes. The conservator could consider Chris unfit to integrate back into society and decide that the best place for him is in the group home.